This invention relates to a method and apparatus for qualitative measurement of minority carrier lifetimes and bulk diffusion length in P-N junction photovoltaic solar cells.
There is a need to qualify P-N junction photovoltaic solar cells as to their ability to convert solar energy into electricity in a manner that may be automated. It has been shown that if a solar cell is subjected alternately to high frequency (blue) and low frequency (red) light pulses, the minority carrier lifetimes of the diffused N layer and of the bulk P material can be measured. Furthermore, the bulk diffusion length can also be ascertained. Since these parameters determine the efficiency of a solar cell, an object of this invention is to provide a method and apparatus for quick and easy quality control of solar cell production.
For an actual determination of lifetimes and diffusion lengths, the equivalent circuit of the P-N junction diode, the diode admittance and the electrical signal pickup impedance must be known. However, it has been discovered that under certain conditions, this knowledge is not necessary for qualitative measurements.
The steady state current of a P-N junction solar cell has been calculated many times. For the spectral region in the neighborhood of 1.5 to 4.4 eV, it consists of two parts, that of the illuminated N layer and that of the P substrate, respectively. The contribution of the N layer to the total current density is given by: EQU j.sub.p = q N.sub..lambda. L.sub.p L.sub..lambda..sup.-1 (G.sub.p - B.sub.p F.sub.p) (1)
where ##EQU1## L.sub..lambda. = absorption length of light of wavelength .lambda. (the inverse absorption coefficient).
L.sub.p = diffusion length of the holes in the N layer. PA1 N.sub..lambda. = Photon flux (number per area and time). PA1 d = depth of the junction (distance of the depletion layer from the surface). PA1 L.sub.s.sbsb.p = D.sub.p /S.sub.p = surface diffusion length where D.sub.p = diffusion coefficient of the holes and S.sub.p = surface diffusion velocity. PA1 q = elementary charge.
Introducing the diffusion length L.sub.n for electrons in the P base and l = T.sub.h -W-d where W is the width of the depletion layer and T.sub.h the total thickness of the cell, the contribution to the current density due to electrons is given by EQU j.sub.n = q N.sub..lambda. A.sub.n.sup.-1 (F.sub.n + L.sub.Sn /(L.sub.n) G.sub.n) e.sup.-(d+W)/ L.sbsp..lambda. (2)
with EQU A.sub.n = sinh (l/L.sub.n) + L.sub.Sn /(L.sub.n) cosh (l/L.sub.n) (2a) ##EQU2## The enormous difference in magnitude of d and l plays an important role in the further development. The sum of eqs. (1) and (2) constitutes the total current.
Considering now nonstationary irradiation, suppose a beam of monochromatic light with time varying intensity in the neighborhood of 4.4 eV is irradiating the solar cell. With d + W .perspectiveto. 0.3.mu. and L.sub..lambda. .perspectiveto. 10.sup.-2 .mu. we have e.sup.-(d+W)/ L.sbsp..lambda. .perspectiveto. e.sup.-30 and according to eq. (2), the current produced by the P material j.sub.n is negligible. In this case, only the N layer contributes. The opposite is true for a photon energy of 1.5 eV. Here L.sub..lambda. .perspectiveto. 100.mu. and e.sup.-(d+W) /L.sbsp..lambda. .perspectiveto. e.sup.-3 10.sup.-3 .perspectiveto. 1. All light reaches the P base and, since the length or thickness of the base is a thousand times that of the N layer, almost all current will be generated in the P base. Accordingly, it is convenient to split the analysis into two parts: high frequency (blue light) and low frequency (red light).